Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.
– Brian Greene
As a maths graduate I’ve always thought that, although I’ve forgotten most of what I learnt, my studies gave me a really strong analytical mind, a well structured thought process, and better logical reasoning, which has stood me in good stead ever since.
So it was excellent going to this talk to have my suspicions confirmed.
Dr Matthew Inglis of the Royal Society gave the talk to show his evidence that “studying maths develops your thinking skills, logical reasoning and ability to resolve problems”
More specifically he laid out the evidence that the more you study maths, the more you are able to spot flaws in an argument.
The idea that learning anything is good in itself, due to the way it trains intelligence, attitudes and values, is called the Theory of Formal Discipline. Some psychologists dismiss this idea, maintaining that what we learn is specific to the domain to which it applies and is not transferable, however Inglis has confirmed that the theory is true in the case of Maths.
Interestingly, he showed that people who study up to A Level are more able to spot logical flaws, however are subject to false positives, i.e. they are likely to find fault in an argument that is correct.
However, once studying maths to degree level, that excess is moderated, leaving someone able to find fault accurately.
After Inglis finished his talk there was a shockingly small-minded question. A woman said she liked the idea of having her children learn maths, but was worried this would limit their creative capabilities.
She clearly hasn’t studied much maths.
One of the subjects I loved at university was number theory – we often commented on the creativity needed to come up with a proof for a theorem. Mathematicians often talk about the beauty of maths – the ability to express complex concepts simply is brilliant, some even say poetic.
Besides anyone who’s studied Bach will know that his tunes are very mathematical. Often people who study maths are musical and visa versa, for example me!
I suspect part of the issue is that many people hold the belief that says emotion and creativity is distinct from logic and rationality, fed by the old left-brain right-brain myth. This is a bad idea, and quite harmful I feel. The idea that we cannot use knowledge creatively, or apply logic to emotion, is to limit what we are capable of. Simon Baron Cohen has shown that logic and empathy are not mutually exclusive.
What doesn’t help is that people seem to fear maths. I genuinely don’t understand why this is the case. When I told people I was studying maths at university many people would react with awe, saying I must be super intelligent. If I probed they would go on to reveal a real fear of the subject. I must admit, that although I’ve always found maths fun, it was substantially helped by my brilliant maths teacher Mrs Landon who would bounce into lessons, and excitedly tell us that she had “a super mega-equation” to teach us, that was “really powerful and exciting”. Her enthusiasm was infectious. And the principles she taught were simple. A good teacher does make a world of difference.
Bharati Krishna said “It is magic until you understand it, and it is mathematics thereafter“.
So, to get back to the subject, as Plato argued, mathematics should be taught to people to improve their reasoning skills, and as a foundation for the rest of their learning.